This paper is devoted to compute the energy-momentum densities for two exact solutions of the Einstein field equations by using the prescriptions of Einstein, Landau-Lifshitz, Papapetrou and Möller. The spacetimes under consideration are the Weyl-Lewis-Papapetrou and the Levi-Civita metrics. The Weyl metric becomes the special case of the Weyl-Lewis-Papapetrou solution. The Levi-Civita metric p...

Distinguished involutions in the affine Weyl groups, defined by G. Lusztig, play an essential role in the Kazhdan-Lusztig combinatorics of these groups. A distinguished involution is called canonical if it is the shortest element in its double coset with respect to the finite Weyl group. Each two-sided cell in the affine Weyl group contains precisely one canonical distinguished involution. In t...

Electrons in materials with linear dispersion behave as massless Weyl- or Dirac-quasiparticles, and continue to intrigue due to their close resemblance to elusive ultra-relativistic particles as well as their potential for future electronics. Yet the experimental signatures of Weyl-fermions are often subtle and indirect, in particular if they coexist with conventional, massive quasiparticles. H...

A hallmark of Weyl semimetal is the existence of surface Fermi arcs. An intriguing question is what determines the connectivity of surface Fermi arcs, when multiple pairs of Weyl nodes are present. To answer this question, we show that the locations of surface Fermi arcs are predominantly determined by the condition that the Zak phase integrated along the normal-to-surface direction is . The Za...

Weyl points, as monopoles of Berry curvature in momentum space, have captured much attention recently in various branches of physics. Realizing topological materials that exhibit such nodal points is challenging and indeed, Weyl points have been found experimentally in transition metal arsenide and phosphide and gyroid photonic crystal whose structure is complex. If realizing even the simplest ...

The discrete cosine and sine transforms are generalized to a triangular fragment of the honeycomb lattice. The two-variable orbit functions of the Weyl group A2, discretized simultaneously on the weight and root lattices, induce the family of the extended Weyl orbit functions. The periodicity and von Neumann and Dirichlet boundary properties of the extended Weyl orbit functions are detailed. Th...

In this paper explicit decompositions are provided of the Weyl reflections in affine Lie algebras, in terms of fundamental Weyl reflections. PACS: 02.20.Sv; 11.25.Hf

— In this work we extend a previous work about the Weyl asymptotics of the distribution of eigenvalues of non-self-adjoint differential operators with small multiplicative random perturbations, by treating the case of operators on compact manifolds.

We study the asymptotic behavior of the counting function of tensor products of operators, in the cases where the factors are either pseudodifferential operators on closed manifolds, or pseudodifferential operators of Shubin type on R, respectively. We obtain, in particular, the sharpness of the remainder term in the corresponding Weyl formulae, which we prove by means of the analysis of some e...

Incomplete cusp edges model the behavior of the Weil-Petersson metric on the compactified Riemann moduli space near the interior of a divisor. Assuming such a space is Witt, we construct a fundamental solution to the heat equation, and using a precise description of its asymptotic behavior at the singular set, we prove that the Hodge-Laplacian on differential forms is essentially self-adjoint, ...